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Article
Existence of Strong Solutions of a P(X) -Laplacian Dirichlet Problem without the Ambrosetti-Rabinowitz Condition
Computers & Mathematics with Applications
  • Qihu Zhang, Zhengzhou University of Light Industry
  • Chunshan Zhao, Georgia Southern University
Document Type
Article
Publication Date
1-1-2015
DOI
10.1016/j.camwa.2014.10.022
Disciplines
Abstract

In this paper, we consider the existence of strong solutions of the following p(x)-Laplacian Dirichlet problem via critical point theory:

We give a new growth condition, under which, we use a new method to check the Cerami compactness condition. Hence, we prove the existence of strong solutions of the problem as above without the growth condition of the well-known Ambrosetti–Rabinowitz type and also give some results about multiplicity of the solutions.

Citation Information
Qihu Zhang and Chunshan Zhao. "Existence of Strong Solutions of a P(X) -Laplacian Dirichlet Problem without the Ambrosetti-Rabinowitz Condition" Computers & Mathematics with Applications Vol. 69 Iss. 1 (2015) p. 1 - 12
Available at: http://works.bepress.com/chunshan_zhao/20/